Existence of close pseudoholomorphic disks for almost complex manifolds and an applications to Kobayashi-Royden pseudonorm

Details Existence of close pseudoholomorphic disks for almost complex manifolds and an applications to Kobayashi-Royden pseudonorm Existence of close pseudoholomorphic disks for almost complex manifolds and an applications to Kobayashi-Royden pseudonorm

2000-02-23

arxiv.org/abs/math/0002190v1

Functional Analysis and Its Applications, v.33, no.1 (1999), pp.38-48

Mathematics

Complex Variables

18 pages; enlarged version of dg-ga/9708012

Scientific paper

In this paper we extend the notion of the Kobayashi-Royden pseudonorm for almost complex manifolds. Its basic properties known from the complex analysis are preserved in the nonintegrable case as well. The main theorem on coincidence of the pseudodistance induced by this pseudonorm with the Kobayashi pseudodistance for the almost complex manifold is equivalent to the possibility of deforming slightly a pseudoholomorphic disk in an almost complex manifold. We also describe the result in terms of h-principle and consider a geometric application for moduli spaces of pseudoholomorphic curves.

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